Currently, the digital signature technique commonly used is RSA signature mechanism, and its security is established on the difficulty of large number factoring. However, with constant improvement of computer process power and sustained development of related researches, RSA has to continuously increase digits of modulus N to ensure the security, from 512 bits to 1024 bits, further to 2048 bits. Because of the excess length of key bits, the operation for generating big prime number and exponential computation becomes more complex, therefore, the efficiency of RSA is not very high. If the hardware is employed to improve the efficiency, the excess length of bits will result in more complexity and higher cost, and due to the unchangeability of hardware, the use life of hardware becomes shorter, which further increases the cost as a result.
Since Ki Hyoung K O, Sang Jin Lee of Korea proposed a key exchange protocol and public encryption system based on the difficulty of braid groups conjugacy problem (K. H. Ko, S. J. Lee, J. H. Cheon, J. W. Han, J. S. Kang and C. S. Park, New Public-Key Crytosystem Using Braid Groups, Proc. of Crypto 2000, LNCS 1880, Springer-Verlag (2000) 166-183.), the braid public key cryptography system is widely researched. However, there has been no good solution for its digital signature scheme. Up to 2003, Ki Hyoung K O, Doo Ho Cho, the scholars of Korea, proposed and realized two signature schemes based on braid conjugacy problem (Ki Hyoung Ko and Doo Ho Choi and Mi Sung Cho and Jang Won Lee New Signature Scheme Using Conjugacy Problem Cryptology ePrint Archive: Complete Contents 2003/168): simple conjugacy signature scheme (SCSS) and conjugacy signature scheme (CSS). We will explain the two signature schemes of SCSS and CSS.
Simple conjugacy signature scheme SCSS:    Common parameter: braid group Bn, hash function h: {0,1}*→Bn     Key generation: public key: a conjugacy pair (x,x′)εBn×Bn for considering CSP problem as a difficult problem,            private key: aεBn, meeting x′=a−1xa;            Signature: for a given bit sequence message M, the signature of M sign(M)=a−1ya, in which, element y=h(M);    Verify: the signature of message M sign(M) is legal when and only when: sign(M)˜y and x′ sign(M)˜xy.
However, since a hacker may get many pairs of (yi, a−1yia), it may result in blowing the gab of private key a, i.e., k-CSP problem. In order to overcome the above problem, they proposed a CSS signature scheme.
Conjugacy signature scheme CSS:    Common parameter: braid group Bn, hash function h: {0,1}*→Bn     Key generation: public key: a conjugacy pair (x,x)′εBn×Bn for considering CSP problem as a difficult problem,            private key: aεBn, meeting x′=a−1xa;            Signature: for a given message M, selecting a random braid bεBn at random, calculating α=b−1xby=h(M∥α), β=b−1yb, γ=b−1aya−1b, the signature of message M sign(M)=(α, β, γ).Verify: the signature of message M sign(M)=(α, β, γ) is legal when and only when meeting α˜x, β˜y, αβ˜xy, αγ˜x′y.
Due to the introduction of random braid b, CCS signature scheme overcomes the k-CSP problem well. But due to the increase of calculation and data, the overall efficiency is decreased distinctly.